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Compound Interest (Without using formula) — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSCompound Interest (Without using formula)5 Marks
Question
On a certain sum of money, the difference between the compound interest for a year, payable half$-$yearly, and the simple interest for a year is $Rs. 180/-$ Find the sum lent out, if the rate of interest in both the cases is $10\ \%\ $ per annum.
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Answer

Let principal $p= Rs. 100 ; R=10\ \%\  ; T=1$ year
$\text { SI }=\frac{100 \times 10 \times 1}{100}=\text { Rs. } 10 \text {. }$
$\mathrm{Cl}$ payable at every 6 months
So, $R=\frac{10}{2}=5 \%$
$I=\frac{100 \times 5 \times 1}{100}=\text { Rs. } 5$
$A=100+5=\text { Rs. } 105$
For second year
$P=\text { Rs. } 105$
$I=\frac{105 \times 5 \times 1}{100}=\text { Rs. } 5.25$
Total compound interest $=5+5.25= Rs. 10.25$
Difference of $\mathrm{Cl}$ and $\mathrm{SI}=10.25-10= Rs. 0.25$
When difference in interest is $Rs. 0.25$ , sum $= Rs. 100 .$
If the difference is $Rs. 1$ then
sum$=\frac{100}{0.25}$
If the difference is $Rs. =180$ then
 sum $=\frac{100}{0.25} \times 180=\text { Rs. } 72,000$

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